What is the derivative [sin x]
Cos x
The derivative of [sin x], where [ ] represents the floor function or greatest integer function, is not defined for integer values of x. This is because the floor function changes abruptly at integer values, causing a discontinuity in the derivative.
However, for non-integer values of x, we can take the derivative of sin x and then round down to the nearest integer. This gives us:
[d/dx [sin x]] = cos x
Therefore, for non-integer values of x, the derivative of [sin x] is equal to the floor of cos x.
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